All journalists like seeing their articles discussed on television, even when they're being challenged, but the sight of John Poppleton holding a copy of an obituary I wrote earlier this year for the Guardian made me feel profoundly ashamed.

The subject was Father Kit Cunningham, the Catholic priest who had married us, baptised my son (who shares his Christian name) and was a family friend for 20 years. "A Technicolor eccentric, and widely loved as a consequence," the obituary read.

"I find this," Poppleton said, brandishing the newspaper cutting to camera as if it were contaminated, "offensive. This priest was a monster."

Poppleton had been repeatedly sexually abused as a young boy by Fr Kit, an experience that he says "broke me down and broke my spirit". The abuse took place at St Michael's, Soni, in the 1960s, in what was then Tanganyika, now Tanzania. Four of the priests who taught there, all members of the Rosminian order, and including Fr Kit, perpetrated physical and sexual abuse that made this boarding school, according to Poppleton, "a loveless, violent and sad hellhole".

He is not alone in his trauma. In Abused: Breaking the Silence, a documentary to be shown on BBC1 on Tuesday, reporter Olenka Frenkiel hears from other former pupils at Soni about how they were subjected to a regime of sexual abuse from which they were powerless to escape. Some of them, grown men, break down in tears on camera as they recall being photographed naked, hauled out of bed at night to have their genitals fondled, and worse.

I say worse because I struggle to repeat what I heard, and to reconcile the Fr Kit that Poppleton describes with the amiable, kindly, dedicated parish priest I knew for the years, long after Soni, when he was rector of St Etheldreda's, the oldest Catholic church in London.

In my obituary of him in January, I wrote as I found. A week after publication I received an email. "It is good that he is remembered for his good," my correspondent began, "but there are many who will remember the other side of Kit… a sexual, physical and mental abuser. It would be good if you just let him rest in peace, but I finally reacted as there was too much praise going on for this deviated creep."

Deviated creep? In almost three decades of writing about the church, and a lifetime as part of it, I thought I knew how to read a priest. Since the 1990s, when the scandal of paedophile priests first emerged in the public domain, a question mark has been hanging over almost every cleric as a result of the church's cover-up. Almost every priest, but not, for me, foolishly imagining myself a seasoned observer, over Fr Kit. His vices appeared pretty obvious – drink, obsessive attention to restoring his church, and what looked like an overly close friendship with the (female) parish secretary, who shared his love of wine. But here was a letter telling me Fr Kit was a paedophile.

My first (shameful) instinct was to wonder if my correspondent might be mistaken, but he had included in his note a means of testing his claim. "Suffice it to say," he wrote of Fr Kit, "he returned his MBE to the Queen last year when his past demons came to haunt him." That was something I could check easily. It was true.

A correspondence developed. I am not going to name the other party because he made clear he didn't want that. He is not part of the group of 22 ex-pupils of Soni pursuing a legal case for compensation against the Rosminians. But he was abused there, as was his brother, or so he believes. The two have never discussed it.

As part of that correspondence, I saw the letters of apology written by Fr Kit before his death, and by the other accused (all of whom are still alive, and living in a comfortable retirement home run by the Rosminians in the home counties). They are also shown in the documentary. All are general in tone and claim not to remember specifics or individuals. Perhaps they have blotted them out, or perhaps they have been told by a lawyer not to incriminate themselves. "Poor", "vague", "not from the heart" are the onscreen reactions to these mea culpas from their victims. "I'd like to hear a lot more," one comments.

In one sense the story of Soni is another appalling example of a by now sadly familiar tale. I say that not to play down the suffering of the victims, but rather to acknowledge that the torment of Poppleton and his fellow pupils at St Michael's mirrors the experience of many others, widely reported, at the hands of abusive paedophile priests.

There have also been repeated public expressions of regret by the Catholic authorities as these scandals have emerged all round the globe, revealing this as an endemic problem in the church rather than, as Pope John Paul II originally suggested in 2002, a case of a few bad apples.

Bishops and cardinals have pledged to confront past wrongs, to work with victims to address their pain and to set up procedures to make sure nothing of this kind ever happens again. However, Frenkiel points out in her film that on the day that Pope Benedict XVI, during his visit to Britain last September, was in Westminster Cathedral expressing his "deep sorrow to innocent victims of these unspeakable crimes", the Rosminian order was writing to refuse to pay any compensation for what it has openly acknowledged are the crimes of four of its own priests.

There is a running debate that takes place at the gates of my children's Catholic primary school. "What are we doing?" parents ask each other, "sending our children to a school run by the Catholic church when we are reading about the abuse in its schools elsewhere that it has covered up?"

The ready answer – and I have been as ready as anyone else to utter it – is that most allegations concern episodes several decades ago, our school is a warm, loving, nurturing place, governed by extremely strict rules of conduct (I am the safeguarding governor) and that, more broadly, Catholicism in Britain has set up a system to ensure no abuser will ever again use the church to prey on children.

Then I found out about Father Kit and it has shaken me out of my complacency and shaken my faith – shaken it because here is a religious order still reluctant to own up to the damage its members have done. The Rosminians appear, to this Catholic at least, to be placing defending the institution – ie their order, its good name and its properties – above a heartfelt acceptance of the catalogue of depression, broken marriages and suicide attempts recounted by victims in the documentary. Yes, I know that compensation money doesn't wipe the slate clean, but it is the most common way our society has of shouldering the blame.

And shaken it too because I felt that Fr Kit was a priest I could trust. If he kept his "dark side" so well hidden, if the church authorities allowed him to keep it so well hidden that even the Queen awarded him an MBE, what of all the other priests I admire for their work with the poor and marginalised? Who can I trust now when my children go into the sacristy to be altar-servers? And if I am struggling to trust priests, what on earth am I doing in the church at all?

Such questions might nag away slightly less insistently if I thought the Catholic authorities were genuinely trying to understand the root causes of this scandal. But this month the quasi-official Catholic Truth Society published a booklet on clerical sex-abuse that blames it on the "permissive society" of the 1960s. So while everyone else took sexual liberation to mean you didn't have to wait until you were married, priests took it as licence to abuse children?

When I think about Fr Kit today, as well as a powerful feeling of betrayal, happy memories of time in his company continue to crowd in, making me feel as if I am part of that culture of cover-up and denial of abuse. It is probably a process that everyone goes through who discovers, out of the blue, that a trusted family friend is an abuser. How to reconcile my image, there in our wedding pictures, of genial Fr Kit with the younger, slimmer version photographed at Soni in old home-movie footage, unmistakable in his TV-screen specs, but soon to abuse another helpless boy? So far, it has proved impossible.

The church would urge greater understanding of human frailty and forgiveness. On a broader canvas, that distinctive demand for forgiveness in a secular society that is ever more punitive keeps me going to mass every Sunday. But for forgiveness, there must also be genuine acknowledgement of the damage done. Privately returning your MBE when on your deathbed, without explanation, doesn't quite count. Neither does refusing compensation, or holding a memorial service for Fr Kit where not a word of this scandal was breathed.

As an institution, despite claiming to have turned over a new leaf, the church – still, falteringly and often uncomfortably my church – emerges from this particular story as failing distressingly to practise what it preaches.